Question

A magazine reported the results of a random telephone poll commissioned by a television network. Of the 1359 men who​ responded, only 18 said that their most important measure of success was their work.

Complete parts a through c.

a) Estimate the percentage of all males who measure success primarily from their work. Use a ​95% confidence interval.​ Don't forget to check the conditions first.

(__________%,_______________%)​

(Type integers or decimals. Round to one decimal place as​ needed.)

b) Some believe that few contemporary men judge their success primarily on work. Suppose we wished to conduct a hypothesis test to see if the fraction has fallen below the ​8% mark. What does your confidence interval​ indicate? Explain. Choose the correct answer below.

A. Since ​8% is not in the​ interval, there is strong evidence that fewer than ​8% of all men use work as their primary measure of success.

B. Since ​8% is in the​ interval, there is strong evidence that fewer than ​8% of all men use work as their primary measure of success.

C. Since ​8% is not in the​ interval, there is strong evidence that more than ​8% of all men use work as their primary measure of success.

D. Since ​8% is in the​ interval, there is strong evidence that more than 8​% of all men use work as their primary measure of success.

What is the level of significance of this​ test? Explain.

The level of significance is $\alpha =$ __________. The test is a(a) (1)___________ test based on a (2)___________

(1) lower-tail, upper-tail, two-tail

(2) 99.9% confidence interval. 95% confidence interval. 97.5% confidence interval. 99% confidence interval.

Answer 1

conditions to construct confidence interval

a) if sample size (n) is less than or equal to 5% of the population size (N); and

b) n(p̂)(1 - p̂) ≥ 10

both are satisfied

Favorable Cases X = 18 Sample Size N = 1359 The sample proportion is computed as follows, based on the sample size N = 1359 and the number of favorable cases X = 18: X N 18 1359 0.013 The critical value for a = 0.05 is Zc = 21-a/2 = 1.96. The corresponding confidence interval is computed as shown below: CI(Proportion) (---*1 = 4*,*+ =V6.-) = 0.013 - 1.96 x 0.013(1 – 0.013) 1359 0.013 + 1.96 x 0.013(1 – 0.013) 1359 = (0.007,0.019)

A. Since ​8% is not in the​ interval, there is strong evidence that fewer than ​8% of all men use work as their primary measure of success.

alpha= 0.05

Z test based on population proportion

95% confidence interval

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